V/I uppercase/lowercase convention?

Question

Is there any standard in industry for using uppercase or lowercase for V and I in circuit diagrams? I ask this because my book seems to switch back and forth between the two without any rhyme or reason and I can't figure out any pattern for why it will choose one way over the other. It also switches back and forth for subscripts.

Answer 1

I agree with you that it is important to know the meaning of the different ways for using such symbols. And the same applies also to the voltage-to-current ratios (resitances, impedances). For my opinion the standard is (or should be) as follows:

• Uppercase (V,I) for DC and rms values
• Uppercase for ohmic resistors R=V/I
• Lowercase (v,i) for signals as a function of time: v(t), i(t)
• Lowercase (v,i) for (small) differential signals available for a certain DC bias point only.
• Lowercase (r) for differential (dynamic) small-signal resistances r=v/i.

As a negative example, in small-signal equivalent circuits, sometimes the inverse transconductance gm of a BJT is used as Re=1/gm. This is very confusing because this does not represent any (ohmic) resistor and, more than that, can be mixed-up with an external emitter resistor RE.

EDIT/UPDATE: Regarding impedances:

For reactive elements (L, C) the voltage-to-current ratios are called "impedance". Because this applies to rms values of sinusoidal signals only the symbol for impedances also is written in uppercase letters Z=V/I.

Answer 2

I'll add a couple of points to the good answers you've already received:

quantities obtained applying various kind of transforms to the time domain signal should be uppercase, specifically:

• Phasors, i.e. complex representation of sinusoidal signals.

• Frequency-domain signals, i.e. Fourier transforms of time-domain signals. For example the frequency response of a system and related input and output signals or the like:

  • \$Y(f) = H(f) \cdot X(f) \$
  • \$V_o(\omega) = G(\omega) \cdot V_i(\omega) \$

• s-domain signals, i.e. Laplace transforms of time-domain signals. For example the transfer function of a system and related input and output signals or the like:

  • \$Y(s) = H(s) \cdot X(s) \$
  • \$V_o(s) = G(s) \cdot V_i(s) \$

• z-domain signals, i.e. Z-transformed signals corresponding to discrete-time signals (e.g. as used in digital signal processing). For example the transfer function of a digital system and related input and output signals or the like:

  • \$Y(z) = H(z) \cdot X(z) \$

Answer 3

I can't find a link to a book that I had referred that talked of such notation conventions. But the closest that came to that standard books was this wikipedia page.

It says,

Large-signal DC quantities are denoted by uppercase letters with uppercase subscripts. For example, the DC input bias voltage of a transistor would be denoted V_IN.

Small-signal quantities are denoted using lowercase letters with lowercase subscripts. For example, the input signal of a transistor would be denoted as v_in.

Total quantities, combining both small-signal and large-signal quantities, are denoted using lower case letters and uppercase subscripts. For example, the total input voltage to the aforementioned transistor would be : v_IN(t)=V_IN+v_in (t).

And,

A large signal is a DC signal (or an AC signal at a point in time) that is one or more orders of magnitude larger than the small signal and is used to analyse a circuit containing non-linear components and calculate an operating point (bias) of these components.
A small signal is an AC signal superimposed on a circuit containing a large signal.